I am an engineer-turned-school-maths teacher....
I love to see the sparkles of understanding in the eyes of my students.... It is really exciting to see I was part of this enlightenment process.... I find myself both inspired and inspiring!
I love doing math with children & sharing my love of math and children with parents and teachers... Check the websites www.about.me/rupesh.gesota and www.supportmentor.weebly.com to know more about me & my math-adventures...

Thursday, September 18, 2014

Playing Maths, again: "Yes! It is Minus 6."

It was the day of Rakhi. This time my sister was not going to visit our place as she had planned to host all the bhai-behens from her in-laws family, at her home. Being aware about this situation, I reach her home on time – I mean, directly at lunch time, and with no surprise - only to be received by new faces with staring eyes but wide smiles. The confusion was evident.

“Hello Rupesh.... Why so late?........... He is my cousin”, came a happy familiar voice from somewhere inside and I then confidently (or still reluctantly?) dragged my feet, straight into bed-room and guess what? This space too was hijacked by few strangers, but this time – the very beautiful and adorable ones – Children!!

“Maaamaaaaa.....!” and here comes my bhaanjaa (Jash) running to me, and then pulling me into his new gang, while proudly showing his Rakhis and gifts he had given to his sisters. The energy and enthusiasm quickly connects us and I was now Mama to all the bacchha-party there J Most of them were toddlers and hence watching them talk and play is a fantastic amusement, in itself and even a good learning for me, quite often. So I decide to lie down, to enjoy this free entertainment, while scrolling through my handset.

But soon I felt someone is whispering to me -- “Mama, do you have games in your phone?”

Jash knows by now that I don’t have games on my handset and so he never comes to me for that. So I was surprised hearing this voice. I turn around and find my ‘new niece’ sitting beside me; the quest for game was clearly visible in the tiny eyes and polite tone of this 9-year old, but sadly, I had to disappoint her with a No. I also noticed that she was done with playing with other toddlers, who were now highly engrossed in ‘pakdaa-pakdee’ J

“Do you watch cartoons?”

“Mummy is not allowing to turn on TV”

“Why?”

“She insists, they want to talk and there is already too much noise at home.”

I so much wished to tell her that chit-chat of these adults was audible even at the staircase. But then something strikes me all of a sudden and I modulate my voice.

“You know, I don’t have games. But I have another interesting thing in my phone.”

“What?”

“Guess. You already know it.”

She jumped back near me with eyes stuck on the screen. I open the calculator app and she shouts immediately --

“It’s calculator! I know that. “

I was kind of aware of this response, but still I was somehow confident of taking it ahead in some way to amuse her (or perhaps ‘us’? :-) How can kids be unaware of this interesting tool – calculator esp. when they are constantly navigating in their parents’ gadgets? ‘Interesting’ I say because I have realized, it is indeed interesting to the children of, at least, school-goers. (Do you know why?) I still remember how I and my friend enjoyed in taking the pocket calculators (even the fancy ones with beep sounds or flashing LEDs) in our schools, of course secretly. In fact, I was even once scolded my Mathsteacher for doing so. Silly or funny it may sound, but I and my friend often sat on the last bench to playthe number crunching race ‘using calculator’ J And I, almost always used to lose!

Anyways, focus the camera on my ‘new niece’ now.

“Yes, I too knew that you would knew it.”

“You know, yesterday it was my maths test and I got 9/10”, while saying this she even grabbed the phone (calci) from my hand.

“Oh good, you just lost one mark.”

“I did a silly mistake.” I loved her ‘cursing’ expressions while she said this. But I wonder, if those were originally hers J

“Hmmm...What mistake?”

“I did a mistake in subtraction sum.”

(The rhyming ‘s’ sounded so sweet in her voice that I did not bother to correct her math-vocab at this point.)

“Can you try that on calculator now?”

She was already exploring the ‘new’ calculator. So I thought, probably it would be easy for her to work on this question/idea that I threw at her.

“I don’t remember the question now.”

“Oh ok. Was it a difficult problem?”

“It was with borrow.”

I guess some of you might have already identified yourself with her situation. Even I smiled on hearing this, and really wanted to tell her that – I understand dear. It’s not your problem. It’s not your mistake, if you are getting confused. But instead, I chose something else --

“Can I give you one problem?”

“Yes, but I will do that on calculator. Not with pen and paper.”

“Of course, yes!”

“You are allowed to use the machine!”

“Machine? This is not the machine. This is a calculator!”

And this reminded me of.... 3 idiots! Remember the humorous argument between Rancho and his teacher on his first engineering class.

“50-20”

“That’s so easy. I can even do this even orally. It’s 30”, and while saying this she pressed the numbers and showed me the answer. I could see, she was unhappy with this ‘easy’ question. In fact, I too ‘hate’ giving ‘easy’ questions to students, as much as ‘they hate’ solving ‘easy’ questions.

“Fine. Tell me what 5-2 is?” (This one was, of course, for teasing her ;-)

“And now, she was furious -- I am not in 1st standard. Give me difficult sum.”

“Oh..Ok. Check 2-5” (I swear, I don’t know how this slipped out of my mouth. Perhaps, because of her challenge?)

“What? 2-5 is not possible!” She said to me with confidence, that it is a wrong question.

“Well, can you check this on Calculator?”

Her typing was no-less than a real climax for me now. I don’t know what was she thinking, but I was much more anxious to see her response.

“Oh, it’s 3!” She looked at me with a shock, eyes and mouth wide-open. And then, I too was not waiting for this response!!

Bhoooooom !!! Hopes dashed! What the heck, how can the calculator give a positive solution for 2-5? And in this confusion/desperation, I turned the calculator to me and guess what? Relief! The calculator was not wrong. She had simply ignored the negative sign. J

“Hey, is it 3?”

“Yes, but how come it is 3?”

“Hmm....Can you try typing 5-2 now?”

She did, this time without a word of argument.

“This is also 3.”

“Ok.. Now I want you to type 2-5 again and carefully observe what the answer is?”

She did. “It’s same 3”

“No. It is not just 3. It is something else. Observe carefully.”

Her head turned down. And she again sprang with excitement and wonder in her voice -- “It is Minus 3!”

“Yes. Did you see the difference?”

“Yes, now give me one more sum.”

“Ok. Tell me what will be 10-4?”

“6”

“So then what will be 4-10?”

After thinking for a second, “minus 6?”

But this time she was asking me, she was also smiling, though one could sense some confidence too in her suspicion.

“I don’t know. Just check it.”

She did it. “Yes, it’s minus 6!” and Waaaaow!! Now came the real Joy!! She literally jumped off the bed and this excitement did not just reward me the climax that I was desperately waiting for, but also drove the attention of my nephew Jash into this scene, who was now, I guess, playing video game on his mom’s handset.

“What happened?” he asked in a curious tone.

And before I could say anything, she chipped in. “Do you know what 3-5 is?”

And I was like, stunned. Oh My God! She is going to spread the virus, it seems. And my concern was (or actually, I was not really concerned) that Jash is in class-1 now and is still learning the concepts of 1-digit addition, subtraction and 2-digit numbers.

This simple question as if stimulated Jash to immediately snatch the calculator from her hand. “Yes, I know. It is 2.”

“No, it is minus 2”, she corrected him with a teasing smile.

My eyes were now stuck on Jash, but it seems he did not hear her and was busy pressing the numbers. He typed three keys, ‘3’, ‘-‘ and ‘5’ , but was perplexed to not see the answer on screen. (Guess why? ;-)

“Mama, I am not getting the answer.”

“Arrey stupid, press equal to”, she instructed him while pointing at ‘=’ symbol.

He did and then looked back at her with an arguing tone. “See, I told you it is 2”

She started looking at me, while even laughing aloud. What was she thinking? Did this scene remind her of her own learning journey? Her own confusions? I don’t know. But I was super-enjoying this. A child who has just discovered something interesting is now challenging/ leading (out of pure excitement) another child, her peer, towards this ‘new’ element, and while the latter is still struggling to figure out, the former finds this struggling process interesting enough to remind her of her own learning curve. Isn’t this just amazing?

“Mamaaa.. Tell her. Why is she laughing at me? I got the answer 2.” He complains to me with authority.

“Hey, don’t do that. You should guide him, the way I guided you. Can you?”

She drew his attention towards the minus sign before 2. “See, it is Minus 2. Not 2.”

Oh...this made me a little sad, for a while. Wouldn’t it have been super if this minus was uttered from Jash’s mouth rather than she (his sweet teacher) straightaway ‘explaining’ her? This also reminded me a beautiful quote -- “Teaching is the art of asking right questions!”

Anyways, never mind. As long as it is one from one child to another child, the language/ method is a no problem for me. There is a powerful essence of peer-group learning. Many other interesting things have happened between her and Jash in that process, so it does not matter if that word ‘minus’ has not come out from Jash’s mouth.

Jash looked at me with wonder. “Mama, she is telling -- it is Minus 2. Is she right?”

“What do you feel? Can you see that sign?”

“Yes, it is minus sign.”

I felt that the girl had now, knowingly or unknowingly, wore the hat of her teacher when I found her furthering with him: “What will be 4-10?”

Jash was about to type. And she stopped him. “Tell me the answer without typing.”

He started thinking. After a while, “5!”

She again started giggling, thus again irritating Jash and hence I now had to tap this opportune moment to talk about the Big Lesson (more imp. than Maths!)

And I am glad I could quickly pull them IN back, in a healthy (learning) mood. And this time, I took the charge of Investigation with my new (younger) pupil J

I had realized that he was bit struggling with subtraction of numbers more than 5. But then, I also knew he was able to handle smaller numbers. So teaching him 10-4 was out of my mind for now. That may perhaps dampen the essence of something new and interesting learning happening, something that had captivated and excited both of them.

“Jash, what is 4-3?”

He was about to type. And I stopped him.

“Wait. Tell me first. I know you know the answer.”

After a second: “1”

“Good. You can check now”

He did it and happily flashed it to both of us.

It was time for work and observation now (no other talk) else he would miss the observation (pattern). I quickly continued.

“So what will be 3-4 then?”

He was about to type again and I stopped him. “Think”

The other student looked at me with a smile but this time, there was no masti J

I repeated. “You see 4-3 =1. So what do you feel what would be 3-4?”

He replied in a moment with a blend of confidence (and even a bit of doubt) “ Minus 1”

And before I could even open my mouth, the girl shouted “Yes!”

I can’t tell you how awesome it was for me to see one child finding pleasure in observing the other child learning!

“Can you check it on calculator?”

He did that and the Minus sign did not spare him either. He too screamed. He too jumped.

(And me? I super-jumped! ;-)

I challenged him further with couple of more problems (of course in enthusiastic tone) with smaller numbers, and then even with 10-20 and every time he first thought, then guessed aloud, and then quickly verified on calci on his own and finally screamed in Joy !! Joyful Jash J

“Jash, can you now pose a problem to your sister?”

He gave one instantly, randomly and happily. And she too followed the same steps.

Think. Guess. Verify. Enjoy.

But I followed these steps: Enjoy. Enjoy. Enjoy. Enjoy J

Now she wanted to take turn and pose a problem to Jash, but he was now tired (nothing new, you know! I know the game now ;-) and hence ran away! J So the girl turned at me now for seeking a ‘difficult problem’.

I had no option but to quench her thirst now, or probably even enhance it. I went ahead to bigger (2-digit) numbers. And then even larger like 100-300, 450-650 etc. and my pace and voice and enthusiasm ensured that she would NOT get the time to use calculator. She was more enjoying with this human machine now, as it was giving her a visual feedback (I am enjoying too, when you learn) and we had subtly entered into the zone of Mental Math where we discussed out some interesting strategies to find out the answer of 8-45, 18-45 and so on. (What? You want to listen to this story too? Later ;-)

I was also happy that we could finally, and even intelligently, touched the category that she referred to in the very beginning: “subtraction with borrow’ J but just look at the world we have roamed around.

I have often noticed that students feel delight and it motivates them when you tell them that they have learned something of higher class/grade. So when I told her, “You know, you have done the 6th standard Math in 4th standard itself?” Her excitement knew no bounds and she just zoomed out of that room to share this accomplishment with her mom.

Her mom, a stranger to me, came to me with a surprised look. “What is she saying?”, she asked in a laughing tone. I could only respond with a smile. J

Meanwhile, an amusing thought came to my mind – What will his class-1 teacher do if Jash insists that it 'is possible’ to remove 5 from 2 and in fact, it's equal to ‘Minus 3’? J

Both my pupils had disappeared into another world, leaving me alone with pleasant experiences.... And it was then, when a familiar voice was again heard, finally pulling me too out of the number-land – “Chalo bhai, don’t you want to tie Rakhi?” J

On Thu, Sep 18, 2014 at 6:58 AM, Swati & Agyat wrote:Thanks Rupesh for sharing this. I had heard about maths being poetry....now it seems it is also prose....this looks like a book in makingI remember Anjali telling me about writing stroies for Science.....

V v interesting. I vividly remember how my grandson kabeer wowed a class of math teachers in Istanbul Turkey in November 2012, when I asked him what was a certain position on the number line to the left of zero. He looked, thought for a moment, and whispered in my ear- "Is it minus half?". The whole class clapped spontaneously! He was right !He was in class 3 at that time and bunking school to accompany his grandfather to Turkey.Dr. Vivek